A stacked neural network approach for yield prediction of propylene polymerization

A Stacked Neural Network Approach for Yield Predictionof Propylene Polymerization

Seyed Ali Monemian,1 Hamed Shahsavan,2 Oberon Bolouri,1 Shahrouz Taranejoo,1

Vahabodin Goodarzi,1 Mahmood Torabi-Angaji1

1School of Chemical Engineering, University of Tehran, Tehran, Iran2Chemical and Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran

Received 13 April 2008; accepted 7 August 2009DOI 10.1002/app.31251Published online 23 December 2009 in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: Prediction of reaction yield as the most im-portant characteristic process of a slurry polymerizationindustrial process of propylene has been carried out.Stacked neural network as an effective method for model-ing of inherently complex and nonlinear systems–espe-cially a system with a limited number of experimentaldata points–was chosen for yield prediction. Also, effect ofoperational parameters on propylene polymerization yieldwas modeled by the use of this method. The catalyst sys-tem was Mg(OEt)2/DIBP/TiCl4/PTES/AlEt3, where

Mg(OEt)2, DIBP (diisobutyl phthalate), TiCl4, PTES (phenyltriethoxy silane), and triethyl aluminum (AlEt3) (TEAl)were employed as support, internal electron donor (ID),catalyst precursor, external electron donor (ED), and co-catalyst, respectively. The experimental results confirmedthe validity of the proposed model. VC 2009 Wiley Periodicals,Inc. J Appl Polym Sci 116: 1237–1246, 2010

Key words: stacked neural network; modeling;polyolefins; Ziegler–Natta polymerization

INTRODUCTION

Ziegler-Natta catalysts are the most common andimportant commercial catalyst systems to producemillions of tons of polyethylene and polypropyleneto fulfill strong worldwide demand. A considerableproportion of this demand is met by large scale,slurry and gas phase processes. Supported catalystsenable us to use high activity polymerization sys-tems with negligible reactor fouling, and at thesame time, producing polymer powders of goodmorphology and high bulk density.

To obtain a better polymerization behavior, tradi-tional supports such as MgO,1 Mg(OH)2,

2 MgCl2,3

and silica4 have been used; but among them, silicaand MgCl2 have received the most attention and arebeing used immensely in olefin polymerization. Assimple silica supported catalysts have not been ableto polymerize polypropylene successfully,5 magne-sium compounds (especially MgCl2) have beenknown to be the most useful supports. But highhygroscopicity of MgCl2 and high chlorine contentof MgCl2 supported catalysts make its use difficult.Thus, some studies have been conducted to improvecatalyst preparation methods by use of the Magne-

sium Alkoxides to obtain good polymerizationbehaviors. As a result, the chemical reaction methodfor preparation of such catalysts using a Mg(OEt)2/ID/TEAl/TiCl4/ED system have appeared to resultin the most favorable polymerization behavior.6–9

There are only a few records reporting a compre-hensive review on the effect of operational parame-ters on polymerization of propylene to get suitableproductivity and isotacticity index (I.I.%);10–13 there-fore, a thorough study on the effect of operationalparameters on the mentioned systems would be use-ful. According to the fact that process modeling isproved to be successful in many facets of process en-gineering and it can be utilized to reach predictivepurposes, modeling of such a system would be valu-able. As industrial processes behave nonlinearly insome cases, developing of an accurate model forcontrol, optimization, and simulation would be a dif-ficult task. Artificial neural network (ANN) isknown as one of effective methods, capable of mod-eling of inherent complex and nonlinear systems.14

Recently, in some papers focused on the polymer-ization process, the effects of the variables and oper-ating conditions on the final polymer properties andproductivity have been investigated with assistanceof artificial intelligence.15–19

Among the ANN techniques, stack generalizationis a technique for combining neural networks inorder to provide a practical model for prediction. Toimprove the accuracy of model, especially when lim-ited numbers of experimental data points are

Correspondence to: M. Torabi-Angaji ([email protected]).

Journal ofAppliedPolymerScience,Vol. 116, 1237–1246 (2010)VC 2009 Wiley Periodicals, Inc.

available, stacked neural network (SNN) is recom-mended.20 As we knew from literature survey, de-spite its unique characteristics, there is no reportwithin the literature utilizing SNN technique inpolymerization processes.

In this article, Mg(OEt)2 supported catalyst wasprepared and characterized. A comprehensive studyon the effect of operational parameters on the poly-merization behavior of the synthesized catalyst hasbeen implemented. Finally, the effect of the processvariables on the polymerization yield was investi-gated through the proposed SNN model.

EXPERIMENTAL SECTION

Chemicals

Magnesium ethoxide and phenyl triethoxy silanewere purchased from Fluka (Switzerland). DIBP,TiCl4, and toluene (extra pure grade) were pur-chased from Merck (Germany). A 1 M solution ofTEAl was supplied from Schering (Germany). Pro-pylene and nitrogen (99.999% purity) were preparedfrom Arak Petrochemical (Iran). Normal heptaneand n-hexane ([H2O] < 3 ppm) were supplied fromShazand Refinery (Iran).

Preparation of catalyst

Mg(OEt)2 (10 g) and TiCl4 (20 mL) were added to80 mL dried toluene in a 200 mL three-necked flaskvigorously stirring with a magnetic stirrer undernitrogen pressure. Upon reaching 90�C, 2.7 mLDIBP was added as internal donor (ID). The reac-tion was continued for 2 h at 115�C. After decanta-tion, product of the reaction was washed at 40�Ctwo times and each time with 100 mL dried tolu-ene. The same process was carried out at 115�C foranother 2 h and treated in 80 mL toluene with 20mL of excess amount of TiCl4. On completion ofthe process, the catalyst was washed 10 times withn-hexane at 80�C and dried under nitrogen pres-sure. Finally, the mixture of 2 g of washed catalystand 40 mL of dried n-heptane was located underthe nitrogen purge to be injected into polymeriza-tion reactor.

Typical polymerization procedure

Polymerization was conducted in a 1.6 L Buchi typereactor equipped with a mechanical stirrer (adjustedto 500 rpm during the polymerization).After removing all the moisture, air, and impur-

ities by purging with nitrogen, the reactor wascharged with 800 mL n-heptane. Co-catalyst wasinjected into the reactor 5 min after the injection ofexternal donor (ED) solution. Then, catalyst suspen-sion was injected into the reactor and stayed in con-tact with mixture of co-catalyst and ED solutions.The preparation of co-catalyst and ED was done byaddition of 10 mL of 1 M solution TEAl to 63.3 mLand 24 mL of PTES to 76 mL of n-heptane, respec-tively. Finally, solvent was saturated with monomerand warmed upto the desired reaction temperatureand supplied with continuous pressure at the ambi-ent polymerization pressure. The monomer line wasalways set to 10 bar and could be regulated toanother pressure level for a different polymerizationcondition. At the end of polymerization process,produced polymer was weighted after being filteredand dried in vacuum at 70�C.

Catalyst and polymer characterization

Ti and Mg content of the catalyst were determinedby atomic adsorption spectrophotometer (Shimadzu6800). 100–150 mg of the catalyst dissolved in 10 mLof 0.2N sulfuric acid and diluted to 100 mL with dis-tilled water. Chlorine content was measured by Vol-hard’s method.21,22 Chemical microstructure of thecatalyst was obtained by FTIR with an 8 : 1 (w : w)ratio mixture of catalyst to potassium bromide using

Figure 1 FTIR spectra of: (a) Mg(OEt)2, (b) DIBP, (c) Cat-alyst 1, and (d) Catalyst 2. [Color figure can be viewed inthe online issue, which is available at www.interscience.wiley.com.]

TABLE ICatalyst Elemental Analysis Results

Element Wt % in Catalyst 1 Wt % in Catalyst 2

Ti 2.75 2.6Mg 22.01 21.8Cl 58.01 55.36

1238 MONEMIAN ET AL.

Journal of Applied Polymer Science DOI 10.1002/app

Test Scan Series 8000 Shimadzu. Specific surfacearea of the catalyst was measured via BET method.Extraction of precipitated isotactic polymer in boil-ing normal heptane was used to calculate percentageof isospecifity of the polymer as discussed in theliterature.23

Elemental analysis

Table I tabulates elemental analysis for a sample ofthe synthesized catalysts (Catalyst 1). The resultswere compared with an industrial Mg(OEt)2 sup-ported catalyst donated by Arak Petrochemical. (Cat-alyst 2). The results obtained from the synthesizedcatalysts are comparable with the industrial one.

FTIR analysis

FTIR analysis enables us to recognize catalyst chemi-cal structure. Figure 1 shows the resultant spectra.As it is shown in both catalysts spectrum [Fig.1(c,d)], the peak at 1420 cm�1, appearing to corre-spond to Mg(OEt)2, has shifted to 1636 cm�1, corre-sponding absorbance band for MgCl2.

13 It meansthat due to the reaction between ethoxide groupsand TiCl4, a great amount of ethoxide groups havebeen changed to MgCl2. The weak peaks in therange 1300–1500 cm�1 are probably representative ofdifferent types of Mg(OEt)2 or TiCl4-n(OEt)n and theevidence for attendance of residual ethoxide groupsin the form of Mg(OEt)2 and TiCl4-n(OEt)n. The spec-trum for DIBP shows a strong band at 2500 cm�1,which is shifted to 2250 cm�1 in catalysts spectra.24

Specific surface area, porosity, density

Specific surface area of the catalyst was obtainedfrom nitrogen absorption results at different relativepressure levels. According to the observed isothermsthat are in concurrence with Bruner second type iso-therms describing a multi-layer absorption behav-ior,25 the best correlation for the measurement of

these types is BET equation. BET calculation is basedon multi-layer physisorption, whereas Longmuir cal-culation is based on the simple layer physical absorp-tion. Table II compares the BET and Longmuir spe-cific surface areas of Catalyst 1 and Catalyst 2. Asit is obvious, magnificent increase in specific surfacearea was obtained in comparison with industrialcatalyst and data from other investigations onfourth generation Ziegler-Natta catalyst in theliterature.26

In majority of the studies, pore size distribution ofthe catalyst particles is obtained by considering thedesorption branch of nitrogen adsorption isotherms.Here, this quantity was measured using BJH method.Table III shows average pore volume and averagepore diameter for the Catalyst 1 and Catalyst 2.Table IV shows the porosity and bulk density

results for the catalysts. It is apparent that the poros-ity of the Catalyst 2 is less than that of Catalyst 1.

Effect of operational parameters on propylenepolymerization

In this section the effect of operational parameterson propylene polymerization using Catalyst 1 isinvestigated as follows:

Effect of co-catalyst/transition metal molar ratio

As it can be seen in Table V, catalyst activityincreased in terms of the polymerization productiv-ity until reached a maximum and then fell. It wasfound that the addition of Al-alkyl co-catalysts tothe catalyst system and subsequently their interac-tions progressively activated the potential activesites and increased their number, resulting inincrease of the polymerization productivity.27–29

Also, study of different quantitative methods of

TABLE IIIAverage Pore Volume and Diameter

Catalyticsystem

Averagepore volume

Averagepore diameter

Catalyst 1 0.281 35.98Catalyst 2 0.225 35.99

TABLE IIBET and Longmuir Specific Surface Area

Catalytic system BET (m2/g) Longmuir (m2/g)


TABLE IVBulk Density and Porosity

Catalytic system Bulk density (g/cm3) Porosity


TABLE VEffect of Al/Ti Ratio on Propylene Polymerizationa

No. Al/Ti (molar ratio) Yield (Kg PP/(g Ti)ah) I.I.%

1 330 66 98.32 440 68 98.13 520 70 97.54 740 80 97.15 850 58 96.8

a Polymerization conditions: [Ti] ¼ 0.052 mmol/lit, P ¼9 bar, T ¼ 70�C, time ¼ 2 h, agitator speed ¼ 500 rpm

YIELD PREDICTION OF PROPYLENE POLYMERIZATION 1239


determination of Tinþ species in the catalyst systemdemonstrated that the majority (almost 90%) of ini-tial Ti ions on the catalyst surface were of typeTi(IV) reduced to lower valence states such as Ti(III)and even Ti(II) due to alkylation with co-catalystligands.30–35 Besides, industrial and scientific,records show that polymerization of propylene atthe temperatures near 70�C with catalyst systems issimilar to our system, a considerable amount ofactive sites are formed by species of oxidation stateshigher than Ti(II). In fact, for similar catalytic sys-tems, the Ti(II) species are inactive to polymerizepropylene.31,36–38

Therefore, considering the fact that reductionprocesses are fostered due to increase of Al-alkylconcentration, formed active sites may suffer fromdeactivation caused by over-reduction of titaniumspecies form higher oxidation states like Ti(IV) andTi(III) to inactive Ti(II) species during both catalyst/co-catalyst pretreatment and polymerization pro-cess.35,39 Therefore, falling of catalyst activity as aresult of this reality is expectable.

A slight decrease of I.I.% after use of higher con-centrations of co-catalyst might be ascribed byremoval/extraction of ID due to complexation withco-catalyst species, as it is reported in the litera-ture.39 Owing to the fact that the interaction betweenID and Ti species is not very strong,27,40 addition ofhigher amounts of co-catalyst might cause theextraction of a large amount of IDs by formation ofcomplexes with TEAl, and finally resulting trans-form of isospecific Ti-ID complexes to specific

uncomplexed Ti species.39 This is likely the mostreasonable theory to explain the effect of co-catalyston I.I.% of the final polymer.

Effect of co-catalyst/ED ratio

It is well known that use of a Lewis bases as EDremarkably affects the stereospecifity, polymeriza-tion kinetics and the activity of Ziegler-Nattacatalysts.41,42

It is found that addition of the ED to the catalystsystems improves the stereospecifity of the activesites by reversible complexation of it to the coordina-tively unsaturated active sites.43

According to Kakugu et al.,44 there are two kindsof active site structures in the first steps of the poly-merization (a specific active site, which is labeled bystructure 1 in Figure 2 and low-isospecific active siteas labeled by structure 3).They suggest that addition of ED improves the

isospecifity of the catalyst due to transformation of aspecific active centers of structure 1 to high isotacticactive sites of structure 2, resulting in a remarkableincrease in I.I.% of the final polymer. However,simultaneously transformation of structure 3 as aresult of use of high amounts of ED may cause anactivity decrease due to generation of inactive sitesafter transformation of low isotactic active sites toinactive ones under structure 4.Table VI shows the obtained results from poly-

merization of the synthesized catalyst using different

Figure 2 Models for the active centers on supported Ti catalyst and the effect of an ED; (h) Cl vacancy.44

TABLE VIEffect of External Electron Donor on Propylene

Polymerization

No. Al/Si (molar ratio) Yield (Kg PP/(g Ti)ah) I.I.%

1 20 66.8 96.52 16 80 97.13 10 70 97.84 5 64 98.6

a Polymerization conditions: [Ti] ¼ 0.052 mmol/lit, P ¼9 bar, T ¼ 70�C, time ¼ 2 h, Al/Ti ¼ 740, agitator speed ¼500 rpm

TABLE VIIEffect of Monomer Pressure on Propylene

Polymerizationa

No. Pressure (bar) Yield (Kg PP/(g Ti)ah) I.I.%

1 6 32 98.12 7 60.8 97.53 8 70 97.34 9 80 97.15 10 97 97

a Polymerization conditions: [Ti] ¼ 0.052 mmol/lit, T ¼70�C, time ¼ 2 h, Al/Ti ¼ 740, Al/Si ¼ 16, agitator speed¼ 500 rpm



amounts of ED in terms of Al/Si molar ratio. As it isobvious, the productivity of the catalyst increased toa maximum point and then fell because of anincrease in number of inactive sites in higheramounts of ED. But I.I.% of product rose monotoni-cally due to increase in ED amount. Lee et al.27 havereported similar results similar to the observedtrend.

Effect of monomer pressure

By choosing optimum amounts of ED and co-cata-lyst leading to the most polymerization productivityobtained in previous steps of experiments, and 70�Cas the polymerization temperature, a slightly lineardependency of productivity to different pressures inthe range 6–10 bar was being observed, as shown inTable VII. This was due to the fact that higher pres-sure and concentration of monomer causes catalystparticles to break (especially in initial steps of reac-tion) and to locate new created active centers in thepolymerization media.45,46

Effect of temperature

Polymerization was carried out at different tempera-tures in the range 55–80�C. According to Table VIII,due to increase in temperature, activity rose to amaximum point and then began to fall. At high tem-peratures, diffusion is the determining step of poly-merization rate. On the other hand, gas solubility inliquid at high temperatures decreases because of the

increase of molecular kinetic energy of gas.44 Also,that result might be ascribed to naturally irreversibledestruction reaction of active centers takes place athigh temperatures.45

Also, according to Table VIII a considerabledecline of I.I.% for the final polymer took place withincreasing the polymerization temperature. Similarresults are observed in several reports.27,37,47

Effect of reaction time

Productivity rose with extending the polymerizationtime. Most of the polymer production took place atinitial steps of reaction and at final step the rate fellnoticeably according to Table IX.

Effect of hydrogen

In this section, the effect of addition of hydrogenduring the polymerization process was studied.Hydrogen was used as a chain transfer unit to con-trol the molecular weight of the polymer for thecommercial production of polyolefins, such as PPand PE using Ziegler-Natta catalysts. In spite of thefact that the mechanism of the activation behaviorand chain transfer reaction remains obscure,

TABLE VIIIEffect of Temperature on Propylene Polymerizationa

No. Temperature (�C) Yield (Kg PP/(g Ti)ah) I.I.%

1 55 72 98.62 60 73.6 98.23 65 75.6 97.74 70 80 97.15 75 64 95.56 80 50 94.2

a Polymerization conditions: [Ti] ¼ 0.052 mmol/lit, P ¼9 bar, time ¼ 2 h, Al/Ti ¼ 740, Al/Si ¼ 16, agitator speed¼ 500 rpm

TABLE IXEffect of Time on Propylene Polymerizationa

No. Time (h) Yield (Kg PP/(g Ti)ah)

1 1 57.22 2 803 3 107.24 4 1185 5 136

a Polymerization conditions: [Ti] ¼ 0.052 mmol/lit, P ¼9 bar, T ¼ 70�C, Al/Ti ¼ 740, Al/Si ¼ 16, agitator speed¼ 500 rpm

TABLE XEffect of Hydrogen on Propylene Polymerization

No. H2 (cm3) Yield (Kg PP/(g Ti)ah) I.I.%

1 0 80 97.12 50 120 97.03 100 136 96.14 150 148 95.85 200 168 95.1

a Polymerization conditions: [Ti] ¼ 0.052 mmol/lit, P ¼9 bar, T ¼ 70�C, time ¼ 2 h, Al/Ti ¼ 740, Al/Si ¼ 16, agi-tator speed ¼ 500 rpm

Figure 3 Schematic architecture of an ANN. [Color figurecan be viewed in the online issue, which is available atwww.interscience.wiley.com.]



majority of the studies introduce hydrogen as anactivator, increasing polymerization rate and alsocontrolling MW of the polymer. This reality emergesfrom the theory, in which activating effect ofhydrogen can likely be ascribed to regeneration ofactive species following chain transfer with hydro-gen at ‘‘dormant’’ 2, 1-inserted sites.48–52 However,some studies show the detrimental effects of hydro-gen for the rate of polymerization.53 As monomersolubility in the polymer particle enhances as aresult of introduction of hydrogen to thepolymerization media, the rate of polymerization ofpropylene increases in the cases hydrogen as a chaintransfer agent is used.54 Also, it is demonstrated thathydrogen gas can be used for the purpose ofcontrolling not only molecular weight but themolecular weight distribution of the polymer. Thelatter directly depends on the distribution of activespecies with different valence states on the catalystsurface. On the ground that hydrogen produces avariety of valence states for Ti on the catalyst surfacedue to continuous chain transfer reactions, anobvious change in polymerization rate in initial anddeclining periods of polymerization processoccurs.55,56

According to Table X, addition of higher amountsof hydrogen resulted in increased activity of this cat-alytic system. In addition, it shows a sensibledecrease in I.I.% of polymer in presence of higheramounts of hydrogen.

THEORETICAL SECTION

Artificial neural network

ANN is a computer based algorithm inspired byactual neurological system. It is made of intercon-nected elements called nodes or artificial neurons,which are a model of biological neurons. Dependingon their application, many types of ANN architec-tures have been developed, such as, Kohonen, feed-forward, radial basis for applications, such as, selforganizing map, pattern recognition, and functionapproximation.57,58 It has been proven mathemati-cally that feed-forward structure is a universalapproximator.59

A simple Feed-forward ANN has three layers ofneurons. The first layer is called input layer, whichreceives information from outside of the network.The second layer, where most of the calculation hap-pens is known as hidden layer. It may have morethan one layer depending on system complexity.Being hidden for user, the process performed in thehidden layer is known as black box. The last layer iscalled output layer, which receives processed infor-mation from network and sends the result to anexternal receptor.60 Figure 3 shows a four layer feed-forward neural network with 2,4,4,1 neurons ininput, hidden, and output layers, respectively.Each neuron receives information from its inter-

connected neurons by its weight factor and calcu-lates the output by its transfer function or activationfunction (F) as follows:

Out ¼ FXni¼1

ðxixiÞ þ b

!(1)

where xi is input data, xi is weight factor for ithdata, n is number of input data, and b is bias. Fcould be hyperbolic tangent, sigmoid, linear, Gaus-sian function, etc.To have an ANN capable of producing desired

results, its parameters i.e., xi and b should be deter-mined to minimize the error between experimentaldata and produced data. Thus, learning algorithm isapplied to train ANN. Many learning algorithmshave been developed, such as, Conjugate Gradient,Levenberg-Marquardt (LM), and Bayesian learning.Among them, LM algorithm performs faster.61 Totrain ANN, dataset is divided in two parts. One ofthem is for training the network and the other is for

Figure 4 Schematic architecture of a SNN. [Color figurecan be viewed in the online issue, which is available atwww.interscience.wiley.com.]

TABLE XIStatistical Analysis to Assess the Prediction Performance for level-0 Models

Level-0 model ANN1 ANN2 ANN3 ANN4 ANN5

SSE 0.35252 0.75357 0.97634 0.13566 0.64352



testing the trained network. The success in making arobust ANN relies strongly on the choice of the pro-cess variables as well as dataset used for training.There are situations during training process, inwhich the training error reduces while the testingerror is still rather high. This is called overfitting. Toavoid overfitting, two methods have been suggested;one is regularization and the other is early stopping.The latter is used in this study. In this method,another dataset is created besides training and test-ing datasets called validation dataset.62 Training pro-cess will stop if validation error increases.

Modeling a system with ANN does not alwaysguarantee the perfect prediction of the system. Thiscould be due to trapping learning algorithm in localminima, design of neural network architecture orlack of enough experimental data. Thus, it built upthe idea of combining neural networks and stackgeneralization.

Stacked neural network (SNN)

Stack generalization is a technique for combiningneural networks in order to provide a practicalmodel for prediction. To improve the accuracy ofmodel, when limited numbers of experimental datapoints in training dataset are available, SNN is rec-ommended.20 In this method, several types of ANNmodels are combined in order to improve modelperformance. Figure 4 shows a simple architectureof SNN.

ANN models developed from original dataset arecalled level-0 models. For a brief overview of thistechnique, suppose that there are two level-0 mod-els. Original datasets are divided in two subsets.Both level-0 models are designed, trained with firstsubset and tested by the other one so that the perfectarchitecture with minimum error between desiredoutput and calculated output is developed. The out-put of these level-0 models along with the originaloutput data forms a new dataset. This dataset isthen used for modeling of higher level of the stackedstructure i.e. level-1 model.63

There are several approaches to develop a level-1model. A simple approach is to take equal weightfactor for each individual level-0 model.64 Secondway is to combine weighted output of each individ-ual level-0 model presented by the followingequation:

TABLE XIIStatistical Analysis to Assess the Prediction Performance

for Level-1 Model

Method Average Weighted average ANN

SSE 0.57232 0.14692 0.00923

Figure 5 Prediction of the effect of Al/Ti variation onyield by SNN and its comparison with the experimentaldata. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]

Figure 6 Prediction of the effect of ED variation on yieldby SNN and its comparison with the experimental data.[Color figure can be viewed in the online issue, which isavailable at www.interscience.wiley.com.]

Figure 7 Prediction of the effect of H2 variation on yieldby SNN and its comparison with the experimental data.[Color figure can be viewed in the online issue, which isavailable at www.interscience.wiley.com.]



YðXÞ ¼Xni¼1

ðxiyiðXÞÞ (2)

where Y is output of SNN, X is vector of ANN inputdata, n is number of ANN models, and xi is weightfactor for combining the ith ANN set by principalcomponent regression (PCR).64 Third approach iscombining the models by using principal componentanalysis (PCA), where output from level-0 modelsare used as training data to train a new level-1 ANNmodel.20

In this article, five ANN models were developedas level-0 model with different architecture and dif-ferent subset of experimental data. The experimentaldataset was divided in five different subsets. Thefirst ANN model was designed and trained withfirst subset and then tested with the next one. This

procedure was repeated until satisfactory errorbetween desired output and calculated output wasobtained. In this way, the best architecture for cur-rent network was found. The same procedure wasused to design other four ANN models. All the net-works were trained by LM algorithm with earlystopping criteria to avoid overfitting. For each ANN,80% of subset was used for training and the rest20% was used for cross validation. Accuracy evalua-tion of all ANN models was based on sum of squareerror (SSE) between desired output and calculatedoutput. To develop the ANN models, number ofnodes in each hidden layer and number of hiddenlayers were varied as well as number of trainingand testing data in subsets.Therefore, five level-0 models were developed. A

couple of them had one hidden layer with threenodes (ANN1, ANN2). Another couple of them hadone hidden layer with five nodes (ANN3, ANN4)and the last level-0 model had two hidden layerswith three nodes (ANN5). All level-0 models hadsigmoid, hyperbolic tangent and linear activationfunctions in their input, hidden, and linear outputlayers, respectively. Output of these level-0 modelsalong with the original experimental data formed anew dataset for level-1 model.

RESULTS AND DISCUSSION

Results obtained from yield prediction for all fivelevel-0 models are presented in Table XI. For level-1model, three mentioned methods for developing aSNN model were applied and the results are pre-sented in Table XII. As shown in Table XII, amongthese three methods, error of simple average methodis the highest. Error of weighted average method islower than simple average method because eachindividual connection weight is considered in this

Figure 10 Evaluation of the SNN model accuracy. [Colorfigure can be viewed in the online issue, which is availableat www.interscience.wiley.com.]

Figure 8 Prediction of the effect of pressure variation onyield by SNN and its comparison with the experimentaldata. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]

Figure 9 Prediction of the effect of temperature variationon yield by SNN and its comparison with the experimen-tal data. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]



approach. ANN model as third approach shows thebest result due to training and learning from level-0data.

By comparing SSE values in Tables XI and XII, itis observed that though SSE values for level-0 mod-els were not satisfactory, SNN provided the bestperformance.

A case study on the effect of operational parame-ters on propylene polymerization was performed.The performance of SNN model to predict the lim-ited numbers of experimental data is illustrated inFigures 5–9. As it is observed, the experimental datashows pretty good matches with the calculated datafor the all studied operational parameters.

Figure 10 shows yield prediction and its compari-son with the experimental data. It is shown that forlimited amount of experimental data, SNNs devel-oped a model considered as an acceptable yieldprediction.

CONCLUSION

A fourth generation Ziegler-Natta catalyst was pre-pared via chemical reaction method. The effect ofoperational parameters on polymerization of thepropylene polymerization was studied. The obtainedresults showed that there was an optimum molar ra-tio of Al/Ti to obtain the highest yield of polymeri.e., [Al]/[Ti] ¼ 740. The highest activity of the cata-lyst was obtained at about 70�C. Increasing themonomer pressure from 6 to 10bar, increased theproductivity of catalyst, monotonically.

Using a SNN modeling approach to predict thepolymerization yield, the effect of operational pa-rameters on slurry propylene polymerization wasstudied. Statistical analysis was performed to judgeon accuracy of the model. Results obtained from thisstudy showed that the predicted data were matchedwell with the experimental data. The proper resultsuggests that similar models can be used to estimatethe yield of the complex and nonlinear processesversus the process variables.

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A stacked neural network approach for yield prediction of propylene polymerization

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